While we have considered a range of different Hele–Shaw configurations in this article, this is by no means an exhaustive list. Using our numerical scheme, opportunities exist to study configurations which have not previously been considered either experimentally and numerically. For example, while the linearly tapered configuration, discussed in sec:TaperedPlatesRadial, has received significant attention [1]}, [2]}, [3]}, [4]}, including our own study in [5]}, an open question is to determine the effect of tapering the plates for the corresponding blob problem. Our scheme could be used to gain insight the effect of the taper angle on viscous finger development when the fluid is withdrawn compared to the parallel plate case discussed in sec:Complementary. Further, additional physical effects on the interface between fluids could be easily included, such as kinetic undercooling [6]}, [7]} or dynamic wetting effects [8]}, [9]}. Further adjustments could be made to apply the scheme to study controlling instabilities in Hele-Shaws with an elastic membrane [10]}, [11]}, [12]} or with an external electrical field [13]}, [14]} and much more.
